Answer:
Vertex form is f(t) = 4 [tex](t-1)^{2}[/tex] +3 and vertex is (1, 3).
Step-by-step explanation:
It is given that f(t)= 4 [tex]t^{2}[/tex] -8 t+7
Let's use completing square method to rewrite it in vertex form.
Subtract both sides 7
f(t)-7 = 4 [tex]t^{2}[/tex] -8t
Factor the 4 on the right side.
f(t) -7 = 4( [tex]t^{2}[/tex] - 2 t)
Now, let's find the third term using formula [tex](\frac{b}{2} )^{2}[/tex]
Where 'b' is coefficient of 't' term here.
So, b=-2
Find third term using the formula,
[tex](\frac{-2}{2} )^{2}[/tex] which is equal to 1.
So, add 1 within the parentheses. It is same as adding 4 because we have '4' outside the ( ). So, add 4 on the left side of the equation.
So, we get
f(t) -7 +4 = 4( [tex]t^{2}[/tex] -2 t +1)
We can factor the right side as,
f(t) -3 = 4 [tex](t-1)^{2}[/tex]
Add both sides 3.
f(t) = 4[tex](t-1)^{2}[/tex] +3
This is the vertex form.
So, vertex is (1, 3)
Jill has just moved to a new town and wants to share plates of baked goods with her neighbors. She has 20 cookies and 12 brownies to share, and wants to split them equally among the plates with no food left over. What is the greatest number of plates she can make to share?
Answer:
4
Step-by-step explanation:
The greatest number of plates Jill can split the 20 cookies and 12 brownies into can be determined by calculating the highest common factor and 20 and 12
Factors of 12 = 1, 2, 3, 4, 6, 12
Factors of 20 = 1, 2,4, 5, 10, 20
Which number line represents the solution set for the inequality-1/2x>_4
Answer:
B
Step-by-step explanation:
Firstly, we solve for x
-x ≥ 2 * 4
-x ≥ 8
Multiply both sides by -1
x ≤ -8
So we look at the inequality represented by this;
We can see that the correct inequality is option B;
Using the approximation of 5 miles = 8 km
How many km is 22.5 miles?
Answer:
22.5÷5= 4.5
4.5×8= 36
Step-by-step explanation:
22.5÷5=4.5
4.5×8=36
Answer:
36.21024 km are in 22.5 miles you can figure this out because you multiply the length value by 1.609
What is the answer for y?
the answer is in the picture
Does anyone know what graph is correct?
First graph is the correct one.
when x= 1
y=f(x) = -√1 = -1
when x= 2
y= -√2
can someone help me with this?
Answer:
-64 is the 26th number
it's an arithmetic sequence because the difference between the number is constant : -3
they are all -3 in difference
Step-by-step explanation:
an = a1 + (n-1)d
an = the nᵗʰ term in the sequence
a1=the first term in the sequence
d=the common difference between terms
-64 = 11 + (n - 1)-3
-64=11 -3n+3
-78 = -3n
n = 26
The sum of a father's and his son's age is 60. Eight years ago, the father's age was 3 times that of his son. How old is each of them?
Answer:
Father=41
Son=19
Step-by-step explanation:
Father=f
Son=s
f+s=60
Eight years ago would mean that 16 is subtracted from 60 since there is both of them
3s+s=4s
4s=44
s=11
11+8=19
33+8=41
Successive approximation
Which set of rational numbers is arranged from least to greatest? 1 over 5, −1.4, negative 1 over 2, 3
Answer:
[tex]-1.4, -\frac{1}{2}, \frac{1}{5}, 3[/tex]
Step-by-step explanation:
Given
[tex]\frac{1}{5}, -1.4, -\frac{1}{2}, 3[/tex]
Required
Order from least to greatest
We have:
[tex]\frac{1}{5}, -1.4, -\frac{1}{2}, 3[/tex]
Convert all fractions to decimal
[tex]0.2, -1.4, -0.5, 3[/tex]
Now order from least to greatest
[tex]-1.4, -0.5, 0.2, 3[/tex]
Replace fractions
[tex]-1.4, -\frac{1}{2}, \frac{1}{5}, 3[/tex]
James charges $4 per car plus $10 per hour in his car washing business use an equation to describe the earning he receives per car
Answer:
4c+10t
Step-by-step explanation:
c= car
t= time/ hour
Solve for X (line a and b parallel)
Answer:
x=29°
Step-by-step explanation:
as lines are parallel.
external alternate angles are equal.
7x-86=4x+1
7x-4x=1+86
3x=87
x=87/3=29
Between the numbers 15/20 and 35/40 , the greater number is
a. 15/20 b. 20/15 c. 35/40 d. 45/30
Answer:
35/40
Step-by-step explanation:
To compare, both denominator should be same.
[tex]\frac{15}{20}=\frac{15*2}{20*2}=\frac{30}{40}\\\\\\\frac{30}{40} \ < \ \frac{35}{40}\\\\\\\frac{15}{20} \ < \ \frac{35}{40}[/tex]
[tex]\sf{\bold{\blue{\underline{\underline{Given}}}}}[/tex]
⠀the numbers 15/20 and 35/40⠀⠀⠀[tex]\sf{\bold{\red{\underline{\underline{To\:Find}}}}}[/tex]
⠀⠀⠀⠀
the greater number is[tex]\sf{\bold{\purple{\underline{\underline{Solution}}}}}[/tex]
we have to find the greater number between 15/20 and 35/40
To do this,
we have to compare the denominator same.
[tex]\sf{\dfrac{35}{40}=\dfrac{35×1}{40×1}=\dfrac{35}{40} }[/tex] [tex]\sf{\dfrac{15}{20}=\dfrac{15×2}{20×2}=\dfrac{30}{40} }[/tex]According to the question,
we have to find the greatest one
[tex]\sf{\dfrac{35}{40} > \dfrac{30}{40} }[/tex] [tex]\sf{\dfrac{35}{40}>\dfrac{15}{20} }[/tex][tex]\sf{\bold{\green{\underline{\underline{Answer}}}}}[/tex]
⠀⠀
[tex]\therefore\mathrm{\dfrac{35}{40} > \dfrac{15}{20} }[/tex]
⠀⠀
In the history of Major League Baseball, the most valuable player award has been won by players from 7 different countries. which countries were they
Answer:
United States, Canada, Dominican Republic, Cuba, Venezuela, Japan, Panama
Step-by-step explanation:
Taking a look at a list of Major League Baseball most valuable players, the countries are:
United States(most players are US-born).
Canada(Joey Votto in 2010).
Dominican Republic(Albert Pujols and Vlad Guerrero Sr. for example).
Cuba(last Jose Abreu in 2020)
Venezuela(last Jose Altuve in 2017)
Japan(Ichiro in 2001).
Panama(Rod Carew)
Find a recursive rule for the nth term of the sequence.
-10, 2, 14, 26, ...
9514 1404 393
Answer:
a[1] = -10
a[n] = 12 + a[n-1]
Step-by-step explanation:
First differences are ...
2 -(-10) = 1214 -2 = 1226 -14 = 12A constant first difference of 12 means this is an arithmetic sequence. Each term is 12 more than the previous, so the recursive rule is ...
a[1] = -10
a[n] = 12 + a[n-1]
(06.01)Four graphs are shown below: Which graph represents a negative linear association between x and y?
Answer:
Step-by-step explanation:
A negative linear association between x and y means that as x increases, y decreases at the same rate, creating a line with a negative slope. This line will tend from upper left to lower right. 2 of those graphs tend from upper left to lower right, but only one of them is a linear representation. That is graph D.
Which statement is not always true for a parallelogram?
A. Consecutive angles are supplementary.
B. Diagonals are congruent.
C. Opposite sides are congruent.
D. Opposite angles are congruent.
Explanation:
If the diagonals are congruent, then we'd have a rectangle. Any rectangle is a parallelogram, but not the other way around.
If we had a non-rectangular parallelogram, with none of the angles 90 degrees, then the diagonals will not be the same length.
Choices A, C and D are true for any parallelogram (rectangle or not).
Cans of soda at a local store a six-pack of soda costs $2.59 and indivdual cans cost $0.80. What is the maximum of cans of soda that can be purchased for $15
Answer: 30 cans (buy them by the six-pack; so you'd buy 5 six-packs)
==============================================================
Explanation:
Let's say you buy six-packs only. Divide the amount of money you have over the cost per six-pack.
15/(2.59) = 5.7915 which rounds down to 5.
If you buy six-packs only, then you can buy a max of 5 of them. That gets you 5*6 = 30 cans of soda.
-------------
Now let's say you buy individual cans only. We'll use the same idea mentioned earlier but this time divide over 0.80
15/(0.80) = 18.75 which rounds down to 18
We round down because we can't buy that 19th can of soda (note how 19*0.80 = 15.2 which is larger than 15).
So if you buy individual cans only, then you can get a max of 18 cans.
We see that it's better to go with the six-pack option (in the first section) since we can get 30 cans compared to 18 cans.
A pallet of floor tiles contains 60 cases of tiles, and the yard has 10 complete pallets of tile. If you remove 180 cases for one customer how many cases of tiles will be remaining in the yard?
Total cases = total pallets x cases per pallet
Total cases = 60 x 10 = 600 cases
600 cases - 180 cases = 420 cases left
Answer: 420 cases
Find the product
14/4 • 33/10 =
Answer:
Step-by-step explanation:
[tex]\frac{14}{4}*\frac{33}{10}=\frac{7}{2}*\frac{33}{10}\\\\ =\frac{7*33}{2*10}\\\\=\frac{231}{20}\\\\=11\frac{11}{20}[/tex]
The ratio of keepers to animals in the city zoo is 2 : 7. The table shows the current numbers of animals and keepers in the zoo. If 21 more animals are added, how many total keepers are needed to maintain the ratio of keepers to animals?
City Zoo
Number of Keepers Number of Animals
12 42
Answer:
18
Step-by-step explanation:
42+12= 63
63/7=9
9*2=18
Answer:
18
Step-by-step explanation:
plato/edmentum
PLZ HELPPP!!! whoever answers first with a good answer ill mark as brainliest
This is because the nth term is found by adding the previous two terms
F(n) = nth term
F(n-1) = term just before the nth term
F(n-2) = term before the F(n-1) term
F(n) = F(n-1) + F(n-2)
We can re-index values of n to say this equivalent statement
F(n+2) = F(n+1) + F(n)
Based on either equation mentioned, adding F(51) and F(52) will get us F(53). In other words, the 51st and 52nd terms add to the 53rd term.
Can someone help me solve this problem please
Thankyouuuu
Answer:
in picture
Step-by-step explanation:
Brainliest please
Answer:
this is the best way for the question
Write using exponents. Rewrite the expression below in the same sequence.
Answer:
[tex]10^2a^2b[/tex]
Step-by-step explanation:
Exponents are a way of shortening multiplication statements. The exponent represents how many times a term is being multiplied by itself. So, when two terms have the same base it can be written with exponents. For example. 10*10 can be written as [tex]10^2[/tex] because 10 is being multiplied 2 times. Therefore, if we do this with every term you get [tex]10^2a^2b[/tex].
Which is a simplified form of the expression -9(y + 1) + 5y?
A. 4y + 9
B. 6y + 1
C. -14y + 9
D. -4y - 9
Answer:
option D
Step-by-step explanation:
[tex]-9( y+ 1) + 5y\\\\= -9y - 9 + 5y \\\\= -4y - 9[/tex]
Jahlil is 6 inches shorter than 4 times his sister’s height. Jahlil’s height is 70 inches.
Answer:
x = his sister's height = 19 inches
Step-by-step explanation:
Let
x = his sister's height
Jahlil's height is given by the equation:
4x - 6 = 70
4x = 70 + 6
4x = 76
x = 76/4
x = 19 inches
x = his sister's height = 19 inches
Check:
4x - 6 = 70
4(19) - 6 = 70
76 - 6 = 70
70 = 70
I need some assistance please.
Answer:
[tex] 48 - 20x = 9 [/tex]
Step-by-step explanation:
[tex] 2 - \dfrac{5}{6}x = \dfrac{3}{8} [/tex]
Multiply both sides by the LCD which is 24.
[tex] 24(2 - \dfrac{5}{6}x) = 24(\dfrac{3}{8}) [/tex]
[tex] 48 - 20x = 9 [/tex]
Can someone help me with this math homework please!
Answer:
Step-by-step explanation:
What is the product?
Step-by-step explanation:
(3a^2b^7)(5a^3b^8)15a^5b^15hope it helps
stay safe healthy and happy...Answer:
Step-by-step explanation:
Multiply the numbers. For multiplying variables, if they have same variables, add the exponents.
(3a²b⁷)*(5a³b⁸) = 3*5* a²⁺³ *b⁷⁺⁸
= 15a⁵b¹⁵
find the next four terms of the sequence 5, 4, 9, 13, 22
Hello,
It is the Fibonacci 's suit.
[tex]u_1=5\\u_2=4\\u_3=u_1+u_2=5+4=9\\u_4=u_2+u_3=4+9=13\\u_5=u_3+u_4=9+13=22\\u_6=13+22=35\\u_7=22+35=57\\u_8=35+57=92\\u_9=57+92=149\\\\\\\boxed{u_{n+2}=u_{n}+u_{n+1}}\\[/tex]
A movie rental store gives free popcorn to every 40th
customer and a free movie rental to every 45th
customer. Which customer was the first to win both prizes?
Answer:
360th customer
Step-by-step explanation:
To find the customer that will receive both the free popcorn and the free movie rental, we have to list the multiples of 40 and 45 until we get a multiple that is the same for both of them.
Multiples of 40: 40, 80, 120, 160, 200, 240, 280, 320, 360, 400, 440
Multiples of 45: 45, 90, 135, 180, 225, 270, 315, 360
360 is the first multiple that is same for multiples of 40 and 45
So the 360th customer will receive both items.
(Sorry if my explanation is hard to understand. I haven't done this kind of math in a while)
Hope it helps (●'◡'●)
